ANGULAR IMPULSE AND ANGULAR MOMENTUM 281 dicular to the plane. Suppose a point on it to be fixed and find expressions for the resulting angular velocity and impulse imparted. Discuss the expressions for special positions of the fixed point. 4. While a circular plate is moving on a smooth horizontal plane one of the elements of its lateral surface is fixed. Find expressions for the resulting angular velocity and the impulse given by the axis. Discuss. the results for special positions of the axis of rotation. 5. A uniform rod lies on a smooth horizontal plane. Where must a blow be struck so that it rotates about one end? 6. In the preceding problem can the rod be made to rotate about its middle point by a single blow? 7. A circular plate which lies on a smooth horizontal plane is struck so that it rotates about one of the elements of its lateral surface as an axis. Find the position where the blow is applied. 8. Find the center of percussion of a hoop which is free to rotate about an axis perpendicular to its plane. 9. How must a triangular plate, placed on a smooth horizontal plane, be struck so that it may rotate about one of its vertices? GENERAL PROBLEMS. 1. Two particles of equal mass are connected by a string of length I and of negligible mass and placed on a smooth horizontal table so that one of the particles is near an edge of the table and the string is stretched at right angles to the edge. The particle near the edge is given a small displacement so that it begins to fall. Show that the interval of time between the instant at which the second particle leaves the table and the instant at which the string occupies a horizontal position is.< given by 2. A uniform bar of negligible cross-section, which is rotating on a smooth horizontal plane about a vertical axis, strikes an obstacle and begins to rotate in the opposite direction. If L and Lf denote the impulses given by the collision to ,the axis and the obstacle, respectively, co and co' the angular velocities of the bar before and after the collision, I the length and m the mass of the bar, and a the distance of the obstacle from the axis,, show that (a) o>' = eoj;